Details

sample81.0ms

Algorithm

intervals

Results

17.0ms	39×	body	2560	valid
14.0ms	191×	body	80	valid
9.0ms	26×	body	1280	valid
8.0ms	119×	body	80	nan
4.0ms	15×	body	640	valid
1.0ms	7×	body	320	valid
1.0ms	1×	body	5120	valid
0.0ms	2×	body	160	valid

simplify110.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.5b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
25.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-cube-cbrt` `times-frac` `associate-/l*`
6×	`sqrt-prod` `distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `flip--`
3×	`distribute-rgt-neg-in` `diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 77

Calls

4 calls:

106.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
10.0ms	(- (* b b) (* 4.0 (* a c)))
36.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series396.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
62.0ms	(- (* b b) (* 4.0 (* a c)))
110.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
86.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify687.0ms

Counts: 89 → 89

prune385.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.9b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
25.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

67×	`times-frac`
48×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
27×	`add-cube-cbrt`
25×	`add-exp-log`
13×	`associate-/r*` `add-cbrt-cube`
12×	`div-exp`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
9×	`associate-/r/`
8×	`sqrt-prod`
7×	`flip3--` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `distribute-rgt-neg-in` `div-inv`
3×	`rec-exp` `diff-log` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 125

Calls

4 calls:

88.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
14.0ms	(- (* b b) (* 4.0 (* a c)))
27.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series428.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
71.0ms	(- (* b b) (* 4.0 (* a c)))
95.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
109.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.0s

Counts: 137 → 137

prune523.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.9b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt 1) (* (/ a 1) (/ 2.0 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
25.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-exp-log`
22×	`add-cbrt-cube`
14×	`add-sqr-sqrt` `div-exp`
13×	`*-un-lft-identity`
10×	`sqrt-prod` `add-log-exp`
9×	`cbrt-undiv` `add-cube-cbrt`
6×	`times-frac` `prod-exp` `associate-/l*`
5×	`pow1`
4×	`cbrt-unprod`
3×	`flip3--` `diff-log` `associate-/r/` `flip--`
2×	`sub-neg` `sqrt-div` `1-exp` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `frac-times` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `neg-log` `associate-l/` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 83

Calls

4 calls:

38.0ms	(/ (sqrt 1) (* (/ a 1) (/ 2.0 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))))
9.0ms	(- (* b b) (* 4.0 (* a c)))
30.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series414.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(/ (sqrt 1) (* (/ a 1) (/ 2.0 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))))
76.0ms	(- (* b b) (* 4.0 (* a c)))
107.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
90.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify915.0ms

Counts: 95 → 95

prune330.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.9b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (* 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) 2.0) a)
0.6b	(- (* b b) (* 4.0 (* a c)))
1.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
25.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

33×	`times-frac`
26×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
21×	`add-cube-cbrt`
16×	`add-exp-log`
13×	`add-cbrt-cube`
10×	`add-log-exp`
7×	`div-exp` `associate-/l*`
5×	`pow1` `cbrt-undiv` `div-inv`
4×	`sqrt-prod`
3×	`flip3--` `diff-log` `associate-/r*` `flip--`
2×	`sub-neg` `sqrt-div` `prod-exp` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `neg-log` `clear-num` `cbrt-unprod` `associate-/l/`

Counts

4 → 94

Calls

4 calls:

41.0ms	(/ (/ (* 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) 2.0) a)
14.0ms	(- (* b b) (* 4.0 (* a c)))
39.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
18.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series410.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(/ (/ (* 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) 2.0) a)
68.0ms	(- (* b b) (* 4.0 (* a c)))
119.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
80.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify883.0ms

Counts: 106 → 106

prune499.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.9b

regimes315.0ms

Accuracy

88.5% (3.3b remaining)

Error of 8.8b against oracle of 5.5b and baseline of 34.2b

bsearch208.0ms

Steps

Iters	Range		Point
8	1.890514070312107e+96	2.5656331724562416e+99	6.3908203947256215e+97
5	3.3925522353218016e-290	9.424679214662256e-290	3.4532572802096264e-290
6	-5.879772917858402e+57	-1.39221916616404e+57	-2.8364280284857153e+57

simplify848.0ms

end0.0ms

sample3.2s

Algorithm

intervals

Results

863.0ms	865×	body	1280	valid
635.0ms	1073×	body	2560	valid
551.0ms	5911×	body	80	valid
281.0ms	3031×	body	80	nan
176.0ms	460×	body	640	valid
89.0ms	222×	body	320	valid
57.0ms	117×	body	5120	valid
17.0ms	122×	body	160	valid